Search results for "Abelian group"
showing 10 items of 160 documents
Albanese Maps and Fundamental Groups of Varieties With Many Rational Points Over Function Fields
2020
We investigate properties of the Albanese map and the fundamental group of a complex projective variety with many rational points over some function field, and prove that every linear quotient of the fundamental group of such a variety is virtually abelian, as well as that its Albanese map is surjective, has connected fibres, and has no multiple fibres in codimension one.
Polyomino coloring and complex numbers
2008
AbstractUsually polyominoes are represented as subsets of the lattice Z2. In this paper we study a representation of polyominoes by Gaussian integers. Polyomino {(x1,y1),(x2,y2),…,(xs,ys)}⊂Z2 is represented by the set {(x1+iy1),(x2+iy2),…,(xs+iys)}⊂Z[i]. Then we consider functions of type f:P→G from the set P of all polyominoes to an abelian group G, given by f(x,y)≡(x+iy)m(modv), where v is prime in Z[i],1≤m<N(v) (N(v) is the norm of v). Using the arithmetic of the ring Z[i] we find necessary and sufficient conditions for such a function to be a coloring map.
Classifying G-graded algebras of exponent two
2019
Let F be a field of characteristic zero and let $$\mathcal{V}$$ be a variety of associative F-algebras graded by a finite abelian group G. If $$\mathcal{V}$$ satisfies an ordinary non-trivial identity, then the sequence $$c_n^G(\mathcal{V})$$ of G-codimensions is exponentially bounded. In [2, 3, 8], the authors captured such exponential growth by proving that the limit $$^G(\mathcal{V}) = {\rm{lim}}_{n \to \infty} \sqrt[n]{{c_n^G(\mathcal{V})}}$$ exists and it is an integer, called the G-exponent of $$\mathcal{V}$$ . The purpose of this paper is to characterize the varieties of G-graded algebras of exponent greater than 2. As a consequence, we find a characterization for the varieties with …
SURFACE SUBGROUPS OF RIGHT-ANGLED ARTIN GROUPS
2007
We consider the question of which right-angled Artin groups contain closed hyperbolic surface subgroups. It is known that a right-angled Artin group $A(K)$ has such a subgroup if its defining graph $K$ contains an $n$-hole (i.e. an induced cycle of length $n$) with $n\geq 5$. We construct another eight "forbidden" graphs and show that every graph $K$ on $\le 8$ vertices either contains one of our examples, or contains a hole of length $\ge 5$, or has the property that $A(K)$ does not contain hyperbolic closed surface subgroups. We also provide several sufficient conditions for a \RAAG to contain no hyperbolic surface subgroups. We prove that for one of these "forbidden" subgraphs $P_2(6)$, …
Kurzweil-Henstock type integral in fourier analysis on compact zero-dimensional group
2009
Abstract A Kurzweil-Henstock type integral defined on a zero-dimensional compact abelian group is studied and used to obtain a generalization of some results related to the problem of recovering, by generalized Fourier formulae, the coefficients of convergent series with respect to the characters of such a group.
On a class of generalised Schmidt groups
2015
In this paper families of non-nilpotent subgroups covering the non-nilpotent part of a finite group are considered. An A 5 -free group possessing one of these families is soluble, and soluble groups with this property have Fitting length at most three. A bound on the number of primes dividing the order of the group is also obtained.
The probability that $x$ and $y$ commute in a compact group
2010
We show that a compact group $G$ has finite conjugacy classes, i.e., is an FC-group if and only if its center $Z(G)$ is open if and only if its commutator subgroup $G'$ is finite. Let $d(G)$ denote the Haar measure of the set of all pairs $(x,y)$ in $G \times G$ for which $[x,y] = 1$; this, formally, is the probability that two randomly picked elements commute. We prove that $d(G)$ is always rational and that it is positive if and only if $G$ is an extension of an FC-group by a finite group. This entails that $G$ is abelian by finite. The proofs involve measure theory, transformation groups, Lie theory of arbitrary compact groups, and representation theory of compact groups. Examples and re…
Finding Invariants of Group Actions on Function Spaces, a General Methodology from Non-Abelian Harmonic Analysis
2008
In this paper, we describe a general method using the abstract non-Abelian Fourier transform to construct “rich” invariants of group actions on functional spaces.
Henstock type integral in harmonic analysis on zero-dimensional groups
2006
AbstractA Henstock type integral is defined on compact subsets of a locally compact zero-dimensional abelian group. This integral is applied to obtain an inversion formula for the multiplicative integral transform.
Integration of functions ranging in complex Riesz space and some applications in harmonic analysis
2015
The theory of HenstockâKurzweil integral is generalized to the case of functions ranging in complex Riesz space R and defined on any zero-dimensional compact Abelian group. The constructed integral is used to solve the problem of recovering the R-valued coefficients of series in systems of characters of these groups by using generalized Fourier formulas.